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Practice Questions for Exam 1 - Matrices and Linear Algebra | MATH 307, Exams of Mathematics

Material Type: Exam; Class: MATRCES&LINEAR ALGB; Subject: MATHEMATICS; University: Iowa State University; Term: Spring 2005;

Typology: Exams

Pre 2010

Uploaded on 09/02/2009

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Math 307, Section A1
Professor Lieberman
February 18, 2005
PRACTICE FIRST IN-CLASS EXAM
Directions: To receive full credit, you must show all work. You may use a calculator to
do the arithmetic, but you must show all steps in the calculations.
Warning: This test only indicates the number and approximate difficulty of problems on
the actual exam. The topics included in this exam cannot be used to determine what topics
will be on the in-class exam
1. (25 points) Solve the system of linear equations
x2+ 4x3=5,
x1+ 3x2+ 5x3=2,
3x1+ 7x2+ 7x3= 6
using elimination.
2. (30 points) Decide whether the matrix
1 0 2
3 1 4
23 4
is invertible. If it is, find the inverse.
3. (15 points) True or false? If T:R2R2rotates vectors through an angle ϕ, then T
is a linear transformation. Justify your answer.
4. (30 points) Find an LU factorization of the matrix
6 9
4 5.

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Math 307, Section A Professor Lieberman February 18, 2005

PRACTICE FIRST IN-CLASS EXAM

Directions: To receive full credit, you must show all work. You may use a calculator to do the arithmetic, but you must show all steps in the calculations. Warning: This test only indicates the number and approximate difficulty of problems on the actual exam. The topics included in this exam cannot be used to determine what topics will be on the in-class exam

  1. (25 points) Solve the system of linear equations x 2 + 4x 3 = − 5 , x 1 + 3x 2 + 5x 3 = − 2 , 3 x 1 + 7x 2 + 7x 3 = 6 using elimination.
  2. (30 points) Decide whether the matrix 

is invertible. If it is, find the inverse.

  1. (15 points) True or false? If T : R^2 → R^2 rotates vectors through an angle ϕ, then T is a linear transformation. Justify your answer.
  2. (30 points) Find an LU factorization of the matrix [ 6 9 4 5

]